The media spin on how widely Pope Francis disagrees with President Trump is not only exaggerated, it offers no context: the pope had less in common with President Obama, though news reports neglect to say so.
Abortion
No public policy issue is more important for Catholics than abortion: the Catholic Church teaches that it is "intrinsically evil," thus putting it in a select category of sins.
On September 1, 2015, Pope Francis wrote that "Since the first century, the Church has affirmed the moral evil of every procured abortion. This teaching has not changed and remains unchangeable." Prior to becoming pope, Cardinal Jorge Bergoglio said, "The right to life is the first human right. Abortion is killing someone that cannot defend him or herself."
When President Obama was in the Illinois state senate, he led the fight to legalize selective infanticide. He fought against a law that would have required doctors to attend to infants born alive after a botched abortion.
In 2007, presidential candidate Obama told Planned Parenthood that "the first thing I'd do as president is sign the Freedom of Choice Act." It would have arguably forced Catholic hospitals to perform abortions, cutting off federal funds if they refused.
On September 16, 2015, President Obama proved his passion for selective infanticide when he pledged to veto a federal bill that would protect the life of a baby born alive as a result of a botched abortion.
Embryonic Stem Cell Research
Pope Francis said on November 15, 2014 that "We are living in a time of experimentation with life. But a bad experiment." He condemned embryonic stem cell research, saying it uses "human beings as guinea pigs to presumably save others. This is playing with life."
On May 9, 2009, President Obama said that his executive order "will lift the ban on federal funding for promising embryonic stem cell research. We will also vigorously support scientists who pursue this research."
Euthanasia
On May 30, 2015, Pope Francis was quoted saying that "Terrorism, war, violence, but also euthanasia are attacks against life."
When he was a U.S. senator, Obama supported government intervention in the case of Terri Schiavo; he voted to provide the physically disabled woman with nutrition. But in 2008, he said this was the senatorial vote he most regretted.
Gay Marriage
In 2010, when he was an Argentinian bishop, Pope Francis said gay marriage was the work of the devil. He said gay marriage is "a clear rejection of the law of God," and "a move of the Father of Lies."
In 2015, President Obama hailed the Supreme Court decision legalizing gay marriage as "a victory for America."
Gender Ideology
"Gender ideology is demonic!" That is what Pope Francis told Austrian Bishop Andreas Laun in 2014.
In 2016, President Obama tried to use the non-discrimination provisions of Title IX of the 1972 Education Amendments to force religious organizations to perform operations whereby a man acquires the body parts of a female or vice versa.
Religious Liberty
When at the White House in 2015, Pope Francis made a veiled reference to Obama's HHS mandate: it seeks to force Catholic non-profit entities to pay for abortion-inducing drugs, sterilization, and contraception in their healthcare plans. The pope cheerfully noted that Americans are "concerned that efforts to build a just and wisely ordered society respect their deepest concerns and their right to religious liberty."
On August 8, 2012, President Obama said that objections to his HHS mandate, and pleas for religious exemptions, were coming from "the far right."
Conclusion
Not only did Pope Francis have less in common with President Obama than he does with President Trump, there are huge qualitative differences.
How to protect the environment, what to do about refugees, and how to handle illegal immigration are important issues, but when compared to specific Catholic teachings on life and death issues, as well as such critical issues as marriage and the family—to say nothing about our constitutional right to freedom of religion—it is clear that Pope Francis shares more common ground with President Trump than he did with President Obama. But don't look to the media to make this point.